Fiber optic gyroscopes are used to accurately sense rotation of an object supporting such a gyroscope. Fiber optic gyroscopes can be made quite small and can be constructed to withstand considerable mechanical shock, temperature change, and other environmental extremes. Due to the absence of moving parts, they can be nearly maintenance free. Furthermore, they can be highly sensitive to very low rotation rates that can be a problem in other kinds of optical gyroscopes.
A typical fiber optic gyroscope includes a coiled optical fiber wound on a core and about the axis around which rotation is to be sensed. The optical fiber provides a closed optical path in which an electromagnetic wave is introduced and split into a pair of waves that propagate in opposite directions and ultimately impinge on a photodetector. During use, a rotation about the sensing axis of the core provides an effective optical path length increase in one rotational direction, and an optical path length decrease in the other rotational direction. The resulting path length difference results in a phase shift between the waves propagating in opposite directions. This result is generally referred to as the Sagnac effect. In a fiber optic gyroscope, the phase shift resulting from the Sagnac effect is used to determine rotation around the axis. Specifically, waves propagating in opposite directions interfere when recombined and impinge upon photodetector, which measure the intensity of the combined wave. The output of the photodetector, which is a measure of the amount of interference, is used to determine the phase difference in the counter-propagating beams, and thus is used to determine rotation around the axis.
In many fiber optic gyroscopes, the traveling electromagnetic waves are modulated by placing an optical phase modulator in the optical path on one or both sides of the coiled optical fiber. This modulation is used to overcome directional ambiguity by introducing a phase shift to the incoming and outgoing waves in the optical fiber. As one example, the phase modulation is achieved by applying a modulating signal across the electrodes of the optical phase modulator. Typically, the modulating signal is a square wave with a period equal to twice the transit time of the light through the coil. The modulating signal causes the photodetector to measure the intensity at two different points in the raised cosine interferogram. The rotation rate and direction can then be determined by the difference in the emitted intensity at the two different measured points.
Some fiber optic gyroscopes operate in a closed loop manner. In closed loop operation, an additional phase shift, equal and opposite to the rotation-induced phase shift, is introduced in addition to the bias modulation. Specifically, in closed loop operation a servo introduces the feedback phase needed to keep the difference in the emitted intensity at the two different measured points zero. In such a closed loop operation, the rotation rate can then be determined by measuring the feedback phase shift needed to null the difference in the measured photodetector intensities. Closed loop operation has many advantages. For example, the output is more stable and linear compared to open loop operation. Additionally, since the rate is determined by measuring the feedback phase, the resulting output does not depend upon the measured total intensity at the photodetectors, and thus has less susceptibility to variations in intensity from temperature, radiation or vibration.
One issue in closed loop fiber optic gyroscopes is that the phase shift needed to null the intensity difference can increase beyond the output range of the optical modulator. For example, for a constant rate rotation situation the phase shift needed to null the intensity difference would be a continually increasing ramp. However, the amount of modulation that can be provided is limited by the circuitry and the range of the optical modulator. To avoid this problem a reset voltage is added or subtracted to the feedback modulation when the feedback modulation nears the optical modulator drive voltage limit. For example, a reset voltage corresponding to a phase change of 2π a can be added or subtracted from the feedback modulation voltage without generating a rate error. This periodic adjustment of the feedback modulation voltage is generally referred to as a 2π reset.
A key enabling technology to closed loop fiber optic gyroscopes is the optical waveguide device that converts an applied electric signal into an optical phase shift. A number of materials possess the ability to convert an electric field into an optical phase shift, with lithium niobate (LiNbO3) being a commonly used material. An electric field applied across a waveguide formed in the lithium niobate or other suitable material changes the index of refraction in the waveguide thus causing the phase of the optical wave to advance or retard depending on the direction of the applied field. For a hypothetical perfect modulator, the phase modulation φ(t) obtained from an applied voltage V(t) is:
            ϕ      ⁡              (        t        )              =                  π                  V          π                    ⁢              V        ⁡                  (          t          )                      ,where Vπ is the modulator electrical-to-optical gain.
For the perfect modulator, Vπ is constant. Unfortunately, in real modulators, Vπ can often depend upon many environmental factors such as temperature, radiation, and humidity. To account for a varying Vπ, Vπ is typically measured using a variety of modulation techniques. Accurate knowledge of Vπ is needed to ensure perfect 2π steps every time the feedback ramp resets. If the reset overshoots or undershoots 2π, then a rate error is generated.
A problem not addressed by Vπ measurement systems is that Vπ can also depend upon the frequency of the applied voltage. Mechanisms for such frequency dependence include trapped charge in the lithium niobate or absorption of water in the lithium niobate surface. These mechanisms can be affected by humidity, temperature, pressure, radiation, and time. A simple first order time invariant model of the modulator dynamics, written in the Laplace domain, relates the phase modulation φ(s) to the applied voltage V(s)
      ϕ    ⁡          (      s      )        =            π              V        π              ·                                        t            c                    ⁢          s                +        d                                          t            c                    ⁢          s                +        1              ·          V      ⁡              (        s        )            
When d=1 the transfer function is identity and both the step response and the frequency response of the modulator are perfect. When d≠1, the initial step response is still good, corresponding to good high frequency performance, but there is an exponential decay with time constant tc to a steady state value of d times the size of the step input. This decay corresponds to degraded low frequency performance of the modulator. When the closed loop fiber optic gyroscope emits a 2π reset command at the drive voltage limit, the initial modulator response is good. The subsequent changing phase modulation, due to the decay of the modulator's step response, results in a phase shift that is indistinguishable from the rotation-induced Sagnac phase shift. Since rotation is based on the feedback voltage needed to null the induced phase shift, the frequency dependence of Vπ introduces a rate error that can be significant for some applications.
Thus, what is needed is a system and method for reducing the sensitivity of the rate measurement to the frequency dependence of the feedback modulator.